SOLUTION: Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now?

Question 279065: Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now?
Found 2 solutions by oberobic, Mr.Gardner:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
mean = sum / count
mean = 6
count = 6
x = sum
6 = x / 6
x = 36
.
In 10 years, the sum will be x+10 = 36 + 10 = 46
mean = 46 / 6 = 7 2/3 = 7.67
.
Done
Answer by Mr.Gardner(4) (Show Source): You can put this solution on YOUR website!
This is how I answered the question. If you let the siblings be represented by the letters a,b,c,d,e,f (there are six of them including Anita), then you can set up the following equation:
(a+b+c+d+e+f)/6 = 6.
This comes from the formula for a mean.
In ten years, each sibling will have added 10 years to their age, so this is the equation for the mean of their ages ten years from now:
[(a+10)+(b+10)+(c+10)+(d+10)+(e+10)+(f+10)]/6
By adding all of the 10's in the numerator we get:
(60+a+b+c+d+e+f)/6
We can seperate this fraction into:
60/6 + (a+b+c+d+e+f)/6
60/6 = 10 and we know that (a+b+c+d+e+f)/6 = 6, so the answer is:
10+6 = 16.
So in ten years the mean age increased 10 years.
Using the same arithmetic we get that the mean age in 20 years will have increased 20 years, so the answer to the second question is 26.
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